Small-scale turbulent dynamo is responsible for the amplification of magnetic fields on scales smaller than the driving scale of turbulence in diverse astrophysical media. Most earlier dynamo theories concern the kinematic regime and small-scale magn
etic field amplification. Here we review our recent progress in developing the theories for the nonlinear dynamo and the dynamo regime in a partially ionized plasma. The importance of reconnection diffusion of magnetic fields is identified for both the nonlinear dynamo and magnetic field amplification during gravitational contraction. For the dynamo in a partially ionized plasma, the coupling state between neutrals and ions and the ion-neutral collisional damping can significantly affect the dynamo behavior and the resulting magnetic field structure. We present both our analytical predictions and numerical tests with a two-fluid dynamo simulation on the dynamo features in this regime. In addition, to illustrate the astrophysical implications, we discuss several examples for the applications of the dynamo theory to studying magnetic field evolution in both preshock and postshock regions of supernova remnants, in weakly magnetized molecular clouds, during the (primordial) star formation, and during the first galaxy formation.
As the fundamental physical process with many astrophysical implications, the diffusion of cosmic rays (CRs) is determined by their interaction with magnetohydrodynamic (MHD) turbulence. We consider the magnetic mirroring effect arising from MHD turb
ulence on the diffusion of CRs. Due to the intrinsic superdiffusion of turbulent magnetic fields, CRs with large pitch angles that undergo mirror reflection, i.e., bouncing CRs, are not trapped between magnetic mirrors, but move diffusively along the magnetic field, leading to a new type of parallel diffusion. This diffusion is in general slower than the diffusion of non-bouncing CRs with small pitch angles that undergo gyroresonant scattering. The critical pitch angle at the balance between magnetic mirroring and pitch-angle scattering is important for determining the diffusion coefficients of both bouncing and non-bouncing CRs and their scalings with the CR energy. We find non-universal energy scalings of diffusion coefficients, depending on the properties of MHD turbulence.
Direct measurements of three-dimensional magnetic fields in the interstellar medium (ISM) are not achievable. However, the anisotropic nature of magnetohydrodynamic (MHD) turbulence provides a novel way of tracing the magnetic fields. Guided by the a
dvanced understanding of turbulences anisotropy in the Position-Position-Velocity (PPV) space, we extend the Structure-Function Analysis (SFA) to measure both the three-dimensional magnetic field orientation and Alfven Mach number $M_A$, which provides the information on magnetic field strength. Following the theoretical framework developed in Kandel et al. (2016), we find that the anisotropy in a given velocity channel is affected by the inclination angle between the 3D magnetic field direction and the line-of-sight as well as media magnetization. We analyze the synthetic PPV cubes generated by incompressible and compressible MHD simulations. We confirm that the PPV channels intensity fluctuations measured in various position angles reveal plane-of-the-sky magnetic field orientation. We show that by varying the channel width, the anisotropies of the intensity fluctuations in PPV space can be used to simultaneously estimate both magnetic field inclination angle and strength of total magnetic fields.
As the standard gamma-ray burst (GRB) prompt-emission model, the internal shock (IS) model can reproduce the fast-rise and slow-decay features of the pulses in the GRB light curve. The time- and energy-dependent polarization can deliver important phy
sical information on the emission region and can be used to test models. Polarization predictions for the GRB prompt phase with the magnetized IS model should be investigated carefully. The magnetic field of the magnetized IS model is very likely to be mixed and decays with radius. The synchrotron emission in the presence of such a decaying magnetic field can recover the Band-like spectrum of the GRB prompt phase. We investigate the dependence of the polarization of GRB prompt emission on both time and energy in the framework of the magnetized IS model. Due to the large range of parameters, it is hard to distinguish the magnetized IS model and the magnetic-reconnection model through polarization degree (PD) curves. The energy-dependent PD could increase toward the high-energy band for the magnetized IS model, while it decreases to zero above the megaelectronvolt band for the dissipative photosphere model. Therefore, we conclude that the energy dependence of PD can be used to distinguish these two models for the GRB prompt emission. Finally, we find that, independent of the observational energy band, the profiles of the $xi_B-PD$ curve for the time-integrated and time-resolved PDs are very similar, where $xi_B$ is the magnetic field strength ratio of the ordered component to the random component.
The interstellar turbulence is magnetized and thus anisotropic. The anisotropy of turbulent magnetic fields and velocities is imprinted in the related observables, rotation measures (RMs), and velocity centroids (VCs). This anisotropy provides valuab
le information on both the direction and strength of the magnetic field. However, its measurement is difficult especially in highly supersonic turbulence in cold interstellar phases due to the distortions by isotropic density fluctuations. By using 3D simulations of supersonic and sub-Alfvenic magnetohydrodynamic(MHD) turbulence, we find that the problem can be alleviated when we selectively sample the volume-filling low-density regions in supersonic MHD turbulence. Our results show that in these low-density regions, the anisotropy of RM and VC fluctuations depends on the Alfvenic Mach number as $rm M_A^{-4/3}$. This anisotropy-$rm M_A$ relation is theoretically expected for sub-Alfv enic MHD turbulence and confirmed by our synthetic observations of $^{12}$CO emission. It provides a new method for measuring the plane-of-the-sky magnetic fields in cold interstellar phases.
Stars form in molecular clouds in the interstellar medium (ISM) with a turbulent kinematic state. Newborn stars therefore should retain the turbulent kinematics of their natal clouds. Gaia DR2 and APOGEE-2 surveys in combination provide three-dimensi
onal (3D) positions and 3D velocities of young stars in the Orion Molecular Cloud Complex. Using the full 6D measurements, we compute the velocity structure functions (VSFs) of the stars in six different groups within the Orion Complex. We find that the motions of stars in all diffuse groups exhibit strong characteristics of turbulence. Their first-order VSFs have a power-law exponent ranging from $sim0.2-0.5$ on scales of a few to a few tens of pc, generally consistent with Larsons relation. On the other hand, dense star clusters, such as the Orion Nebula Cluster (ONC), have experienced rapid dynamical relaxation, and have lost the memory of the initial turbulent kinematics. The VSFs of several individual groups and the whole Complex all show features supporting local energy injection from supernovae. The measured strength of turbulence depends on the location relative to the supernova epicenters and the formation history of the groups. Our detection of turbulence traced by young stars introduces a new method of probing the turbulent kinematics of the ISM. Unlike previous gas-based studies with only projected measurements accessible to observations, we utilize the full 6D information of stars, presenting a more complete picture of the 3D interstellar turbulence.
Probing magnetic fields in the interstellar medium (ISM) is notoriously challenging. Motivated by the modern theories of magnetohydrodynamic (MHD) turbulence and turbulence anisotropy, we introduce the Structure-Function Analysis (SFA) as a new appro
ach to measure the magnetic field orientation and estimate the magnetization. We analyze the statistics of turbulent velocities in three-dimensional compressible MHD simulations through the second-order structure functions in both local and global reference frames. In the sub-Alfvenic turbulence with the magnetic energy larger than the turbulent energy, the SFA of turbulent velocities measured in the directions perpendicular and parallel to the magnetic field can be significantly different. Their ratio has a power-law dependence on the Alfven Mach number $M_A$, which is inversely proportional to the magnetic field strength. We demonstrate that the anisotropic structure functions of turbulent velocities can be used to estimate both the orientation and strength of magnetic fields. With turbulent velocities measured using different tracers, our approach can be generally applied to probing the magnetic fields in the multi-phase interstellar medium.
The Galactic interstellar turbulence affects the density distribution and star formation. We introduce a new method of measuring interstellar turbulent density spectra by using the dispersion measures (DMs) of a large sample of pulsars. Without the n
eed of invoking multiple tracers, we obtain nonuniversal density spectra in the multi-phase interstellar medium over different ranges of length scales. By comparing the analytical structure function of DMs with the observationally measured one in different areas of sky, we find a shallow density spectrum arising from the supersonic turbulence in cold interstellar phases, and a Kolmogorov-like density spectrum in the diffuse warm ionized medium (WIM). Both spectra extend up to hundreds of pc. On larger scales, we for the first time identify a steep density spectrum in the diffuse WIM extending up to several kpc. Our results show that the DMs of pulsars can provide unique new information on the interstellar turbulence.
Via amplification by turbulent dynamo, magnetic fields can be potentially important for the formation of the first stars. To examine the dynamo behavior during the gravitational collapse of primordial gas, we extend the theory of nonlinear turbulent
dynamo to include the effect of gravitational compression. The relative importance between dynamo and compression varies during contraction, with the transition from dynamo- to compression-dominated amplification of magnetic fields with the increase of density. In the nonlinear stage of magnetic field amplification with the scale-by-scale energy equipartition between turbulence and magnetic fields, reconnection diffusion of magnetic fields in ideal magnetohydrodynamic (MHD) turbulence becomes important. It causes the violation of flux-freezing condition and accounts for (a) the small growth rate of nonlinear dynamo, (b) the weak dependence of magnetic energy on density during contraction, (c) the saturated magnetic energy, and (d) the large correlation length of magnetic fields. The resulting magnetic field structure and the scaling of magnetic field strength with density are radically different from the expectations of flux-freezing.
The turbulence in the diffuse intergalactic medium (IGM) plays an important role in various astrophysical processes across cosmic time, but it is very challenging to constrain its statistical properties both observationally and numerically. Via the s
tatistical analysis of turbulence along different sightlines toward a population of fast radio bursts (FRBs), we demonstrate that FRBs provide a unique tool to probe the intergalactic turbulence. We measure the structure function (SF) of dispersion measures (DMs) of FRBs to study the multi-scale electron density fluctuations induced by the intergalactic turbulence. The SF has a large amplitude and a Kolmogorov power-law scaling with angular separations, showing large and correlated DM fluctuations over a range of length scales. Given that the DMs of FRBs are IGM dominated, our result tentatively suggests that the intergalactic turbulence has a Kolmogorov power spectrum and an outer scale on the order of $100$ Mpc.
